The Killing tower of Kerr-NUT-(A)dS spacetimes is generated using a single 2-form, known as the principal
tensor. The existence of a principal tensor is a nontrivial constraint on spacetime geometry, and the
Kerr-NUT-(A)dS metric is (locally) the most general vacuum spacetime which admits a principal tensor
[1]}, [2]}. In terms of the orthornormal coframe, the principal tensor for the geometry
(REF ) is
\( \mathbf {h} = \sum _{k = 1}^{n} x_{k} \mathbf {e}^{k} \wedge \mathbf {\hat{e}}^{k}.\) 
